Edge Universality of Beta Ensembles

By P. Bourgade, L. Erdős, Horng-Tzer Yau. 2013

177 citations recorded by the source corpus.

We prove the edge universality of the beta ensembles for any $${\beta \ge 1}$$β≥1, provided that the limiting spectrum is supported on a single interval, and the external potential is $${\fancyscript{C}^4}$$C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class $${\fancyscript{C}^4}$$C4.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/337286f9ae74ac611a3ee86182e1aa1dc09c295c

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

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Citations in the corpus

Universality of the Stochastic Airy Operator (2013, methodology): “Concurrent with this paper, those authors have extended their method to prove universality at the edge for ˇ 1 and V that are four times differentiable [5].”
A Dynamical Approach to Random Matrix Theory (2017, methodology): “1 and its proof in [24] required a quite different argument, see Theorem 18.”
Fixed Energy Universality for Generalized Wigner Matrices (2014, methodology): “In particular, we will need rigidity estimates from [3] to prove (2.”
On the principal components of sample covariance matrices (2014, methodology): “On the conditioned measure, level repulsion follows as in [14].”